### 抄録

We consider a compressible viscous fluid effected by general form external force in R^{3}. In part 1, an analysis of the linearized problem based on the weighted-L_{2} method implies a condition on the external force for the existence and some regularities of the steady flow. In part 2, we study the stability of the steady flow with respect to the initial disturbance. What we proved is: if H^{3}-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time.

元の言語 | English |
---|---|

ページ（範囲） | 797-826 |

ページ数 | 30 |

ジャーナル | Journal of the Mathematical Society of Japan |

巻 | 55 |

発行部数 | 3 |

出版物ステータス | Published - 2003 7 |

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### ASJC Scopus subject areas

- Mathematics(all)

### これを引用

*Journal of the Mathematical Society of Japan*,

*55*(3), 797-826.

**On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance.** / Shibata, Yoshihiro; Tanaka, Koumei.

研究成果: Article

*Journal of the Mathematical Society of Japan*, 巻. 55, 番号 3, pp. 797-826.

}

TY - JOUR

T1 - On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance

AU - Shibata, Yoshihiro

AU - Tanaka, Koumei

PY - 2003/7

Y1 - 2003/7

N2 - We consider a compressible viscous fluid effected by general form external force in R3. In part 1, an analysis of the linearized problem based on the weighted-L2 method implies a condition on the external force for the existence and some regularities of the steady flow. In part 2, we study the stability of the steady flow with respect to the initial disturbance. What we proved is: if H3-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time.

AB - We consider a compressible viscous fluid effected by general form external force in R3. In part 1, an analysis of the linearized problem based on the weighted-L2 method implies a condition on the external force for the existence and some regularities of the steady flow. In part 2, we study the stability of the steady flow with respect to the initial disturbance. What we proved is: if H3-norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time.

KW - Compressible fluid

KW - Navier-Stokes equation

KW - Stability

KW - Stationary solution

UR - http://www.scopus.com/inward/record.url?scp=0142118603&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142118603&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0142118603

VL - 55

SP - 797

EP - 826

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 3

ER -